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- W2963680003 abstract "• We study the problem of minimizing epidemic size and duration in SIR models. • We investigate the optimal controls through either vaccination or isolation. • Total amount of resources available during the entire epidemic period is limited. • The optimal controls with limited resources are bang-bang with one or two switches. • Epidemic size and duration may represent conflicting objectives to minimize. The total number of infections (epidemic size) and the time needed for the infection to go extinct (epidemic duration) represent two of the main indicators for the severity of infectious disease epidemics in human and livestock. However, few attempts have been made to address the problem of minimizing at the same time the epidemic size and duration from a theoretical point of view by using optimal control theory. Here, we investigate the multi–objective optimal control problem aiming to minimize, through either vaccination or isolation, a suitable combination of epidemic size and duration when both maximum control effort and total amount of resources available during the entire epidemic period are limited. Application of Pontryagin’s Maximum Principle to a Susceptible–Infected–Removed epidemic model, shows that, when the resources are not sufficient to maintain the maximum control effort for the entire duration of the epidemic, the optimal vaccination control admits only bang–bang solutions with one or two switches, while the optimal isolation control admits only bang–bang solutions with one switch. We also find that, especially when the maximum control effort is low, there may exist a trade–off between the minimization of the two objectives. Consideration of this conflict among objectives can be crucial in successfully tackling real–world problems, where different stakeholders with potentially different objectives are involved. Finally, the particular case of the minimum time optimal control problem with limited resources is discussed." @default.
- W2963680003 created "2019-07-30" @default.
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- W2963680003 date "2019-09-01" @default.
- W2963680003 modified "2023-10-12" @default.
- W2963680003 title "Optimal control of epidemic size and duration with limited resources" @default.
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- W2963680003 doi "https://doi.org/10.1016/j.mbs.2019.108232" @default.
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